A distributed positioning method for unmanned systems under network attacks considering state constraints

Abstract

The present invention discloses a distributed positioning method for an unmanned system considering state constraints under network attacks, comprising the following steps: constructing a kinematic equation for an unmanned system considering state constraints; constructing a sensor measurement mathematical model for deception attack coupled non-Gaussian noise; under the maximum entropy criterion, fusing state constraint information, combining consensus iteration to achieve distributed fusion estimation of multi-sensor information, and obtaining a distributed positioning result for the unmanned system. The present invention solves the problem that conventional estimation algorithms increase or even diverge in estimation errors under network attacks and non-Gaussian noise, fuses inaccurate constraint information to improve positioning effects, and achieves distributed high-precision positioning with high robustness and high scalability.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned system positioning, and in particular to an unmanned system distributed positioning method considering state constraints under network attacks. Background Art

[0002] Unmanned systems have been widely used in various fields such as civil and commercial. Their accurate and reliable positioning information is the basis for subsequent planning, decision-making and control. Unmanned system positioning based on sensor networks is a commonly used positioning method, which can provide high-precision absolute positioning accuracy. On the one hand, due to the refraction, reflection, multipath and other effects of wireless positioning signals, there is serious non-Gaussian interference in the measurement information, which will lead to a decrease in positioning accuracy. On the other hand, due to the vulnerability of communication networks, the risk of malicious attacks on unmanned system positioning systems is increasing. Attackers can inject false measurement information, pollute or even replace real measurement data, use false positioning information to disrupt the operation of unmanned systems, and even cause destructive consequences.

[0003] The document with publication number CN114460534A discloses a positioning method and system based on maximum correlation entropy in an impulse noise environment. This method is derived according to the definition of the correlation entropy criterion. Compared with the traditional positioning method, its positioning performance in an impulse interference environment is improved. The document with publication number CN116592877A discloses a visual-inertial fusion positioning method based on maximum correlation entropy in a complex environment. This method uses image alignment and IMU posture solution strategy to estimate the camera posture, and then uses the extended Kalman filter based on maximum correlation entropy to optimize the posture of IMU and vision. Even in a multivariate noise environment, this positioning algorithm can achieve good positioning accuracy and ensure the safe driving of the vehicle. Both of the above methods improve the positioning accuracy under complex noise, but both consider a single positioning information source and do not consider the scenario of distributed positioning of sensor networks.

[0004] The document with the publication number CN116667817A discloses a positioning method based on the maximum correlation entropy distributed volumetric Kalman filter. The method uses the 1.5-order Taylor expansion information of the maximum correlation entropy to achieve distributed positioning based on a specific network topology, and achieves accurate estimation of the vehicle motion state under non-Gaussian noise. However, the method only considers a relatively idealized information transmission channel, does not consider the impact of external network attacks, and does not fully utilize the constraint information of the unmanned system movement to improve the positioning accuracy. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a distributed positioning method for unmanned systems taking into account state constraints under network attacks, which can fully integrate known state constraint information, realize distributed positioning of unmanned systems under network attacks and non-Gaussian measurement noise interference, and improve the robustness and accuracy of positioning.

[0006] Technical solution: A distributed positioning method for unmanned systems considering state constraints under network attacks, comprising the following steps:

[0007] S1, construct the kinematic equations of the unmanned system considering state constraints;

[0008] S2, introduce Bernoulli variables to construct a sensor measurement mathematical model for deception attack coupled with non-Gaussian noise;

[0009] S3, under the maximum entropy criterion, integrates state constraint information and combines consensus iteration to realize distributed fusion estimation of multi-sensor information and obtain the distributed positioning result of the unmanned system.

[0010] Furthermore, in step S1, based on the kinematic characteristics of the unmanned system and in combination with known motion constraint information, a constrained dynamic equation is established. The specific implementation steps are:

[0011] S11, construct the kinematic equations of the unmanned system:

[0012] x i+1 =F i x i +G i w i

[0013] Among them, x i is the system state variable of the unmanned system at time i, F i is the state transfer matrix at time i, G i is the process noise matrix of the system at time i; w i The mean is zero and the covariance matrix is ​​Q i process noise;

[0014] S2, build state constraint information model:

[0015] n i =M i x i +δ i

[0016] Among them, n i is the constraint variable of the unmanned system at time i, M i is the constraint matrix of the unmanned system at time i; δ i The mean is zero and the covariance matrix is ​​T i Constrained noise.

[0017] Furthermore, in step S2, a binary variable conforming to the Bernoulli distribution is introduced As an indicator of whether the kth sensor is under a deception attack, a sensor measurement mathematical model for deception attack coupled with non-Gaussian noise is constructed, and the expression for calculating the actual measurement value of a single sensor is as follows:

[0018]

[0019] Among them, z k,i represents the actual measurement value of the kth sensor at time i, H k,i is the observation function matrix of the kth sensor at time i; v k,i The mean is zero and the covariance matrix is ​​R k,i The measurement noise of the random variable η k,i It means that the attacker attacks at time i with an unknown probability Inject false data into the kth sensor, let η k,i is a zero-mean, covariance γ k,i A non-Gaussian random sequence.

[0020] Further, in step S3, based on the prior input, each sensor is updated at the corresponding time according to the standard discrete Kalman filter to obtain a local one-step prediction value; then, under the maximum entropy criterion, the state constraint information is integrated and the consensus iteration is combined to realize the distributed measurement update of multi-sensor information to obtain the distributed positioning result of the unmanned system; the specific implementation steps are as follows:

[0021] S31, the kth sensor uses the posterior estimate at time i-1 and the estimated error covariance matrix To perform a partial update:

[0022]

[0023] in, and are the local one-step prediction value and estimation error covariance matrix of the k-th sensor at time i; E represents the matrix transpose;

[0024] S32, iterate the fixed point algorithm for each sensor’s measurement update value, and define the consensus distribution items. Then, according to the network topology, each sensor interacts with its corresponding communication node to complete a limited number of consensus iterations:

[0025]

[0026] Among them, I n represents the identity matrix of dimension n; α k,i(0), β k,i (0) and ρ k,i (0) represents the initial value of the k-th sensor at time i; α k,i (l), β k,i (l) and ρ k,i (l) respectively represent the value after the initial value is iterated l times;

[0027] Represents a diagonal weighted matrix, which is adaptively adjusted according to the residual, and the diagonal elements in the matrix satisfy Φ j,i is a user-defined network topology that satisfies:

[0028]

[0029] in,

[0030] S33, calculate the state estimation value and estimation error covariance matrix of each sensor based on the consensus distribution term:

[0031]

[0032] in, K k,i is the gain matrix of state estimation; α k,i (L), β k,i (L) and ρ k,i (L) represent the mean values ​​of the initial values ​​after L iterations.

[0033] Compared with the prior art, the present invention has the following significant effects:

[0034] 1. The present invention proposes to expand the concept of correlation entropy from variables to vectors. Based on this, the state estimation algorithm is designed to better identify measurement anomalies caused by network attacks or non-Gaussian noise in each measurement data, thereby improving the estimation accuracy.

[0035] 2. The present invention adopts a distributed solution to provide reliable positioning information for unmanned systems, and each sensor only needs to exchange data with adjacent sensors, avoiding the emergence of a fusion center, which matches the characteristics of low bandwidth and limited computing resources of the sensor network;

[0036] 3. The present invention fully integrates the inaccurate state constraint information and converts it into prior information, which can improve the positioning accuracy of unmanned systems in harsh environments such as underground, indoors, and underwater, and ensure the operation tasks of multiple unmanned systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of the algorithm flow of an embodiment of the present invention;

[0038] Figure 2 A schematic diagram of the communication topology structure between 10 sensors for observing the movement of an unmanned system according to an embodiment of the present invention;

[0039] Figure 3 is a position error diagram of an embodiment of the present invention;

[0040] Figure 4 is a speed error diagram of an embodiment of the present invention;

[0041] Figure 5 The figure is a schematic diagram of an unmanned system positioning scenario based on a multi-sensor network according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0043] like Figure 1 As shown, a distributed positioning method for an unmanned system considering state constraints under a network attack specifically includes the following steps:

[0044] Step 1: Unmanned system motion state modeling

[0045] According to the complexity and maneuverability of the unmanned system's movement, the possible movement forms of the unmanned system are analyzed and a model set is constructed. The specific method is as follows:

[0046] Step 11: Construct a model set of multi-unmanned system motion equations:

[0047] x i+1 =F i x i +G i w i (1)

[0048] Among them, x i is the system state variable of the unmanned system at time i, F i is the state transfer matrix at time i, G i is the process noise matrix of the system at time i; w i The mean is zero and the covariance matrix is ​​Q i process noise;

[0049] Step 12: Build a state constraint information model:

[0050] n i =M i x i +δ i (2)

[0051] Among them, n iis the constraint variable of the unmanned system at time i, M i is the constraint matrix of the unmanned system at time i; δ i It is the uncertainty factor in practical applications, specifically expressed as a mean of zero and a covariance matrix of T i Constrained noise.

[0052] Step 2: Build a measurement model

[0053] Based on the conventional measurement equation z=Hx+v, considering that the attacker instantly attacks at time i with an unknown probability The injected false data (i.e., random variable) η of the kth sensor k,i , introduce a binary variable that conforms to the Bernoulli distribution As an indicator of whether the kth sensor is under a deception attack; the actual measurement equation of a single sensor is obtained according to the indicator; the specific implementation steps are as follows:

[0054] Calculate the actual measurement value of a single sensor:

[0055]

[0056] Among them, z k,i represents the actual measurement value of the kth sensor at time i, x k,i It is represented as the state value of the kth sensor at time i, H k,i is the observation function matrix of the kth sensor at time i; v k,i The mean is zero and the covariance matrix is ​​R k,i The measurement noise of the random variable η k,i represents the signal sent by the attacker. Without loss of generality, assume that η k,i is a zero-mean, covariance γ k,i A non-Gaussian random sequence.

[0057] Step 3: Distributed positioning

[0058] Each sensor is updated at the corresponding time based on the prior input at time i according to the standard discrete Kalman filter to obtain a local one-step prediction value; then, under the maximum entropy criterion, the state constraint information is fused and the distributed fusion estimation of multi-sensor information is realized in combination with consensus iteration to obtain the distributed positioning result of the unmanned system; the specific implementation steps are as follows:

[0059] Step 31: The kth sensor uses the posterior estimate at time i-1 and the estimated error covariance matrix To perform a local time update:

[0060]

[0061]

[0062] in, and are the local one-step prediction value and estimation error covariance matrix of the k-th sensor at time i; E represents the matrix transpose.

[0063] Step 32, iterate the fixed point algorithm for each sensor's measurement estimate, and define the terms of consensus distribution. Then, according to the network topology, each sensor interacts with its corresponding communication node to complete a finite number of consensus iterations:

[0064]

[0065] Among them, I n represents the identity matrix of dimension n; α k,i (0), β k,i (0) and ρ k,i (0) represents the initial value of the k-th sensor at time i; α k,i (l), β k,i (l) and ρ k,i (l) respectively represent the value after the initial value is iterated l times; Represents a diagonal weighted matrix, which can be adaptively adjusted according to the residual. The diagonal elements in the matrix satisfy Φ j,i is a user-defined network topology that satisfies:

[0066]

[0067] in,

[0068] Step 33, calculate the state estimation value and estimation error covariance matrix of each sensor based on the consensus distribution term:

[0069]

[0070] Among them, α k,i (L), β k,i (L) and ρ k,i (L) represent the mean values ​​of the initial values ​​after L iterations. K k,i is the gain matrix of the state estimation:

[0071]

[0072] The effectiveness of the present invention is further verified by specific examples below:

[0073] In order to verify the effectiveness of the positioning method proposed in the present invention, this embodiment selects 10 sensors to form a sensor network to realize the positioning of the unmanned system; and adopts the following Figure 2 The network topology structure realizes information interaction.

[0074] The equation of motion is modeled as:

[0075]

[0076] Where, T is the sampling time interval; θ is the actual heading angle; u i is the input of the system at time i.

[0077] The measurement equations of different sensors are:

[0078]

[0079] The constraint parameters satisfied by the system are:

[0080]

[0081] n i =

[00] E (17)

[0082] Among them, θ represents some tiny errors in the constraints in actual engineering.

[0083] In the simulation, this embodiment sets the initial state value of each sensor to x0 = [-400, 30, 100, 10] E , the corresponding error covariance matrix is ​​P = diag([40.010.010.01] E ). In order to better reflect the superiority of this method, the present invention is compared with similar positioning methods, and its positioning error is as follows Figure 3 , Figure 4 As shown in the results, it can be seen that the positioning accuracy obtained by the present invention is significantly better than that of the existing methods.

[0084] like Figure 5 The actual application scenario of this embodiment is shown, which uses multiple sensor base stations with known positions to measure the motion state of the unmanned system, and uses the positioning method of the present invention to achieve accurate positioning of the unmanned system.

[0085] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A distributed positioning method for unmanned systems considering state constraints under network attacks, characterized in that: The following steps are involved: S1, construct the kinematic equations of the unmanned system considering state constraints; S2, introduce Bernoulli variables to construct a sensor measurement mathematical model for deception attack coupled with non-Gaussian noise; S3, under the maximum entropy criterion, integrates state constraint information and combines consensus iteration to achieve distributed fusion estimation of multi-sensor information and obtain distributed positioning results of unmanned systems; In step S1, based on the kinematic characteristics of the unmanned system and combined with known motion constraint information, a constrained dynamic equation is established. The specific implementation steps are as follows: S11, construct the kinematic equations of the unmanned system: x i+1 =F i x i +G i w i Among them, x i is the system state variable of the unmanned system at time i, F i is the state transfer matrix at time i, G i is the process noise matrix of the system at time i; w i The mean is zero and the covariance matrix is ​​Q i process noise; S2, build state constraint information model: n i =M i x i +d i Among them, n i is the constraint variable of the unmanned system at time i, M i is the constraint matrix of the unmanned system at time i; δ i The mean is zero and the covariance matrix is ​​T i Constraint noise; In step S2, a binary variable conforming to the Bernoulli distribution is introduced As an indicator of whether the kth sensor is under a deception attack, a sensor measurement mathematical model for deception attack coupled with non-Gaussian noise is constructed, and the expression for calculating the actual measurement value of a single sensor is as follows: Among them, z k,i represents the actual measurement value of the kth sensor at time i, H k,i is the observation function matrix of the kth sensor at time i; v k,i The mean is zero and the covariance matrix is ​​R k,i The measurement noise of x k,i It is represented as the state value of the kth sensor at time i; The indicator indicating whether the kth sensor is under a deception attack; the random variable η k,i It means that the attacker attacks at time i with an unknown probability Inject false data into the kth sensor, let η k,i is a zero-mean, covariance γ k,i Non-Gaussian random sequence; In step S3, based on the prior input, each sensor is updated at the corresponding time according to the standard discrete Kalman filter to obtain a local one-step prediction value; then, under the maximum entropy criterion, the state constraint information is integrated and the consensus iteration is combined to realize the distributed measurement update of multi-sensor information to obtain the distributed positioning result of the unmanned system; the specific implementation steps are as follows: S31, the kth sensor uses the posterior estimate at time i-1 and the estimated error covariance matrix To perform a partial update: in, and are the local one-step prediction value and estimation error covariance matrix of the k-th sensor at time i; T represents the matrix transpose; S32, iterate the fixed point algorithm for each sensor’s measurement update value, and define the consensus distribution items. Then, according to the network topology, each sensor interacts with its corresponding communication node to complete a limited number of consensus iterations: a k,i (l)=Φ j,k a k,i (l-1) b k,i (l)=Φ j,k b k,i (l-1) r k,i (l)=Φ j,k r k,i (l-1) Among them, I n represents the identity matrix of dimension n; α k,i (0), β k,i (0) and ρ k,i (0) represents the initial value of the k-th sensor at time i; α k,i (l), β k,i (l) and ρ k,i (l) respectively represent the value after the initial value is iterated l times; Represents a diagonal weighted matrix, which is adaptively adjusted according to the residual, and the diagonal elements in the matrix satisfy Φ j,k is a user-defined network topology that satisfies: in, S33, calculate the state estimation value and estimation error covariance matrix of each sensor based on the consensus distribution term: in, K k,i is the gain matrix of state estimation; α k,i (L), β k,i (L) and ρ k,i (L) represent the mean values ​​of the initial values ​​after L iterations.

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